The hazard ratio

The hazard ratio (HR) is defined as

Oe/Ee

The HR is the ratio of the relative hazards of the event in the two groups being compared. It compares the risk (hazard) of an event on the experimental arm (Oe/Ee) at any given time with the risk (hazard) of an event in the control arm at the same time. In this sense the HR can be considered to be a type of relative risk for time-to-event data. Thus, for example, a hazard ratio 0.75 represents a 25 per cent reduction of the risk of an event on the experimental arm compared to the control arm.

Confidence intervals for the hazard ratio can be calculated by considering the logarithm for the hazard ratio, because this is approximately Normally distributed. A 100(1 — a)% confidence interval for the logarithm of the hazard ratio is given by:

loge HR — [Z1—a/2 x SE( loge HR)] to loge HR + [Z1—a/2 x SE( loge HR)], where Z1—a/2 is the upper (1 — a/2) point of the standard Normal distribution. The 100(1 — a)% CI for the HR is then exp (loge HR — [Z1—a/2 x SE( loge HR)]) to exp (loge HR + [Z1—a/2 x SE( loge HR)]).

In the expression above

0 0